A multi-strand flow wound tube heat exchanger

Abstract

A multi-strand flow winding pipe heat exchanger comprises a shell side cylinder, the axial direction of which is the first direction; two groups of heat exchange pipes, namely a first group of heat exchange pipes and a second group of heat exchange pipes, which are spirally wound and arranged in the shell side cylinder along the first direction; two first tube sheets, which are arranged on the first end and the second end of the shell side cylinder to support the two ends of the first group of heat exchange pipes; two second tube sheets, which are arranged on the shell side cylinder corresponding to the two ends of the second group of heat exchange pipes to support the two ends of the second group of heat exchange pipes; the length of the second group of heat exchange pipes in the first direction is smaller than the length of the first group of heat exchange pipes in the first direction, and the second group of heat exchange pipes is arranged corresponding to the local part of the first group of heat exchange pipes; at least one of the two second tube sheets is arranged on the side wall of the middle part of the shell side cylinder. Compared with the prior art, the temperature difference of each tube side medium before and after heat exchange is different.

Description

Technical Field

[0001] This invention belongs to the field of heat exchanger technology, specifically relating to a multi-flow wound tube heat exchanger. Background Technology

[0002] Existing multi-flow wound tube heat exchangers, such as the structure disclosed in Chinese Utility Model Patent No. 201420655906.2, "Novel Multi-Flow Heat Exchanger" (Authorization Announcement No. CN204359171U), include a shell, heat exchange tubes disposed within the shell, and upper and lower tube sheets disposed at both ends within the shell. The two ends of the heat exchange tubes are respectively limited on the upper and lower tube sheets. The shell has a shell-side inlet and a shell-side outlet communicating with the shell cavity. Multiple sets of heat exchange tubes are present, with the portion of each heat exchange tube set located between the upper and lower tube sheets spirally wound along the axial direction of the shell. Corresponding to each heat exchange tube set, the shell has multiple tube-side outlets and tube-side inlets communicating with each heat exchange tube set. In use, different tube-side media can be introduced into each heat exchange tube set, simultaneously exchanging heat with the fluid in the shell side, thus improving heat exchange efficiency.

[0003] However, existing multi-flow wound tube heat exchangers have the following unresolved technical problems:

[0004] The flow path of the medium in each heat exchanger tube is similar, resulting in similar temperature differences before and after heat exchange for each tube. However, under certain operating conditions, the medium in each tube needs to be heated or cooled at different temperatures; for example, the temperature difference before and after heat exchange for the first tube needs to be greater than that for the second tube. Existing multi-flow wound tube heat exchangers cannot meet the requirements under these conditions. Summary of the Invention

[0005] The first technical problem to be solved by the present invention is to provide a multi-flow wound tube heat exchanger that provides different temperature differences before and after heat exchange of the medium in each tube, in light of the current state of the prior art.

[0006] The second technical problem to be solved by the present invention is to provide a multi-strand wound tube heat exchanger to improve heat exchange efficiency.

[0007] The technical solution adopted by the present invention to solve the first technical problem mentioned above is: a multi-strand flow wound tube heat exchanger, comprising:

[0008] The shell-side cylinder has a first end, a second end, and a middle section located between the first end and the second end, and the axial direction of the shell-side cylinder is denoted as the first direction and the radial direction as the second direction;

[0009] Two sets of heat exchange tubes, namely the first set of heat exchange tubes and the second set of heat exchange tubes, are spirally wound and arranged in the shell-side cylinder along the first direction;

[0010] Two first tube sheets are respectively disposed on the first end and the second end of the shell-side cylinder to support the two ends of the first set of heat exchange tubes;

[0011] Two second tube sheets are disposed on the shell-side cylinder corresponding to the two ends of the second set of heat exchange tubes to support the two ends of the second set of heat exchange tubes.

[0012] Its features are:

[0013] The length of the second group of heat exchange tubes in the first direction is less than the length of the first group of heat exchange tubes in the first direction, and the second group of heat exchange tubes corresponds to a partial arrangement of the first group of heat exchange tubes.

[0014] At least one of the two second tube sheets is disposed on the side wall of the middle part of the shell-side cylinder.

[0015] In this way, the medium in each tube can be fed into each group of heat exchange tubes as needed. Since the length of the second group of heat exchange tubes is less than that of the first group of heat exchange tubes, the flow path of the medium in the second group of heat exchange tubes is less than that of the medium in the first group of heat exchange tubes. As a result, the temperature difference of the medium in the second group of heat exchange tubes before and after heat exchange is less than that of the medium in the first group of heat exchange tubes, thereby achieving different temperature differences for each medium before and after heat exchange.

[0016] In this invention, the second set of heat exchange tubes may be set at the middle of the first set of heat exchange tubes, or at the end of the first set of heat exchange tubes, or at both the middle and one end of the first set of heat exchange tubes.

[0017] Preferably, the first group of heat exchange tubes has a first spiral segment and a second spiral segment arranged along a first direction, and the second group of heat exchange tubes is arranged corresponding to the first spiral segment.

[0018] Furthermore, the portion containing the first helical section of the first set of heat exchange tubes and the second set of heat exchange tubes in the shell-side cylinder is designated as the first part, and the portion containing the second helical section of the first set of heat exchange tubes in the shell-side cylinder is designated as the second part. The inner diameter of the first part is larger than that of the second part. This achieves the following technical effects: 1. The inner diameters of the first and second parts of the shell-side cylinder are designed accordingly based on the tube winding situation, resulting in a more compact overall structure; 2. The larger inner diameter of the first part facilitates assembly and subsequent inspection and maintenance.

[0019] Preferably, the first set of heat exchange tubes further includes a first straight tube section located between the first spiral section and the second spiral section to connect the first and second spiral sections.

[0020] Preferably, the first straight pipe section is provided corresponding to the first part of the shell-side cylinder.

[0021] Furthermore, one of the second tube sheets is disposed on the side wall of the middle part of the shell-side cylinder, corresponding to the first straight tube section.

[0022] Furthermore, a manhole for personnel to enter and exit is provided on the side wall of the first part of the shell-side cylinder at the position corresponding to the first straight pipe section. This facilitates inspection and maintenance.

[0023] In the above schemes, the shell-side cylinder can be laid horizontally or vertically. Preferably, the shell-side cylinder is arranged vertically, and the first part and the second part of the shell-side cylinder are arranged one below and one above.

[0024] In the above schemes, the second set of heat exchange tubes can be sleeved around the outer periphery of the first set of heat exchange tubes. Preferably, the first set of heat exchange tubes is spirally wound layer by layer from the inside out to form a multi-layer spiral tube, and the second set of heat exchange tubes is spirally wound in each layer of the spiral tube along the spiral direction of the first set of heat exchange tubes. This ensures the heat exchange effect of each set of heat exchange tubes.

[0025] To further address the second technical problem mentioned above, preferably, it also includes:

[0026] Multiple third heat exchange tubes are arranged along the second direction around the end of the first group of heat exchange tubes and inside the shell-side cylinder;

[0027] Two third tube sheets are arranged opposite each other on the radial sides of the shell-side cylinder and adjacent to the first tube sheet used to support the ends of the first set of heat exchange tubes, so as to support the two ends of the third heat exchange tubes.

[0028] The ends of the first set of heat exchange tubes can be either the two ends of the first set of heat exchange tubes or one of the ends, preferably the end corresponding to the shell-side medium inlet side.

[0029] In existing technologies, the heat exchange efficiency at the shell-side end of the shell is relatively low. The design of the third heat exchange tube in this invention overcomes this technical problem and utilizes the space at the shell-side end to improve shell-side heat exchange efficiency. Furthermore, because the third heat exchange tube is arranged along the second direction, the flow path of the tube-side medium within the third heat exchange tube is shorter, allowing for better control of the temperature difference before and after heat exchange by the tube-side medium. This temperature difference differs from the temperature differences before and after heat exchange in the first and second sets of heat exchange tubes. Simultaneously, since the third heat exchange tube is located along the second direction around the end of the first set of heat exchange tubes, it can play a role in flow equalization, improving the fluid distribution of the shell-side medium at the shell-side end (more uniform distribution), thereby reducing heat exchange dead zones.

[0030] Preferably, multiple third heat exchange tubes are divided into two groups, and are arranged in a C-shape with the C-shaped openings facing each other, surrounding the ends of the first group of heat exchange tubes from the inside out on both radial sides.

[0031] Furthermore, the end of the first set of heat exchange tubes is a second straight tube section extending along the first direction;

[0032] It also includes:

[0033] A support cylinder is sleeved on the outer periphery of the second straight pipe section and fixed relative to the first tube sheet used to support the end of the first set of heat exchange tubes. The support cylinder has multiple through holes spaced apart on its wall.

[0034] The third heat exchange tube is arranged around the periphery of the support cylinder.

[0035] The support cylinder can constrain the ends of the first set of heat exchange tubes, preventing them from shaking during heat exchange. At the same time, the support cylinder can also support the third heat exchange tube, and the through holes on the support cylinder allow the shell-side medium to flow.

[0036] Furthermore, the inner and outer adjacent third heat exchange tubes are bound together by gaskets, and the innermost third heat exchange tube is bound to the support cylinder by gaskets, with each gasket extending along the first direction.

[0037] Furthermore, the shell-side cylinder includes a straight cylinder extending along the first direction and a hemispherical end cap disposed on the port of the straight cylinder. The end of the hemispherical end cap is provided with the aforementioned first tube sheet, and the side wall of the hemispherical end cap is provided with the aforementioned third tube sheet and a shell-side connector for the shell-side medium to pass through.

[0038] The third heat exchange tube is located inside the hemispherical head.

[0039] Preferably, the hemispherical head is located at the upper end of the straight cylinder, and the overall structure formed by the multiple third heat exchange tubes is smaller at the top and larger at the bottom, thus matching the shape of the hemispherical head. This allows the third heat exchange tubes to effectively utilize the space within the hemispherical head.

[0040] Compared with the prior art, the advantages of the present invention are as follows: by designing the length of the second set of heat exchange tubes to be less than the length of the first set of heat exchange tubes, and by setting the second set of heat exchange tubes to correspond to a partial arrangement of the first set of heat exchange tubes, the tube-side medium can be input into each set of heat exchange tubes as needed, so that the flow path of the tube-side medium in the second set of heat exchange tubes is less than the flow path of the tube-side medium in the first set of heat exchange tubes, thereby making the temperature difference of the tube-side medium in the second set of heat exchange tubes before and after heat exchange less than the temperature difference of the tube-side medium in the first set of heat exchange tubes before and after heat exchange, thus achieving different temperature differences of each tube-side medium before and after heat exchange. Attached Figure Description

[0041] Figure 1 This is a schematic diagram of the structure of Embodiment 1 of the present invention;

[0042] Figure 2 This is a schematic diagram of the structure of Embodiment 2 of the present invention;

[0043] Figure 3 for Figure 2 Enlarged view of a local structure in the image;

[0044] Figure 4 This is a schematic diagram of the support cylinder in Embodiment 2 of the present invention;

[0045] Figure 5 This is a partial structural cross-sectional view of Embodiment 2 of the invention;

[0046] Figure 6 for Figure 5 Top view of a local structure;

[0047] Figure 7 for Figure 5 Enlarged view of the left side of the cross-section;

[0048] Figure 8 This is a schematic diagram of the structure of the pad strip in Embodiment 2 of the invention;

[0049] Figure 9 This is a partial cross-sectional view of the spacer strip and the third heat exchange tube in Embodiment 3 of the invention. Detailed Implementation

[0050] The present invention will be further described in detail below with reference to the accompanying drawings and embodiments.

[0051] Example 1: As Figure 1 As shown, this is a preferred embodiment of a multi-flow wound tube heat exchanger of the present invention. The multi-flow wound tube heat exchanger includes a shell-side cylinder 1, heat exchange tubes, a first tube sheet 4, and a second tube sheet 5.

[0052] The shell-side cylindrical body 1 is vertically arranged (i.e., the first direction described in the claims and specification of this invention), having a first end 11 at the upper end, a second end 12 at the lower end, and a middle portion 13 located between the first end 11 and the second end 12. The shell-side cylindrical body 1 is composed of a first part 1a and a second part 1b arranged vertically, with the inner diameter of the first part 1a being larger than the inner diameter of the second part 1b. The lower end of the first part 1a is the second end 12 of the shell-side cylindrical body 1, and a first tube sheet 4 is provided thereon. The second part 1b has a vertically extending straight cylindrical body 101 and a hemispherical end cap 102 located at the upper port of the straight cylindrical body 101. The upper end of the hemispherical end cap 102 is the first end 11 of the shell-side cylindrical body 1, and the first tube sheet 4 is provided thereon. Shell-side connecting pipes 103 for the shell-side medium to pass through are provided on both the hemispherical end cap 102 and the second end 12 of the shell-side cylindrical body 1.

[0053] A second tube sheet 5 is provided on the side wall of the middle part 13 of the shell-side cylinder 1 (that is, the side wall of the upper part of the first part 1a) and at the position adjacent to the second end 12 of the shell-side cylinder 1.

[0054] There are two sets of heat exchange tubes, namely the first set of heat exchange tubes 2 and the second set of heat exchange tubes 3, which are spirally wound in the shell-side cylinder 1 in a vertical direction. Specifically, the first set of heat exchange tubes 2 is spirally wound layer by layer from the inside out to form a multi-layer spiral tube, and the second set of heat exchange tubes 3 is spirally wound in each layer of the first set of heat exchange tubes 2 along the spiral direction of the first set of heat exchange tubes 2. At the same time, the first set of heat exchange tubes 2 has a second straight tube section 24, a first spiral section 21, a first straight tube section 23, a second spiral section 22, and a third straight tube section 25 arranged from bottom to top. The first spiral section 21 and the first straight tube section 23 are located in the first part 1a of the shell-side cylinder 1, and the first straight tube section 23 is opposite to the second tube sheet 5 on the side wall of the shell-side cylinder 1. The second spiral section 22 is located in the second part 1b of the shell-side cylinder 1. The upper end of the second straight tube section 24 and the lower end of the third straight tube section 25 are respectively supported on their respective first tube sheets 4. The second set of heat exchange tubes 3 is disposed in the first part 1a of the shell-side cylinder 1 corresponding to the first spiral section 21, and the two ends of the second set of heat exchange tubes 3 are respectively supported on two second tube sheets 5, so that the length of the second set of heat exchange tubes 3 in the vertical direction is less than the length of the first set of heat exchange tubes 2 in the vertical direction.

[0055] Furthermore, a manhole 10 for personnel to enter and exit is provided on the side wall of the first part 1a of the shell cylinder 1 at the position corresponding to the first straight pipe section 23.

[0056] In use, the two tube-side media can be input into their respective groups of heat exchange tubes as needed. Since the flow path of the tube-side media in the second group of heat exchange tubes is shorter than that in the first group of heat exchange tubes, the temperature difference of the tube-side media in the second group of heat exchange tubes before and after heat exchange is smaller than that in the first group of heat exchange tubes, thus achieving different temperature differences for each tube-side media before and after heat exchange.

[0057] Example 2:

[0058] like Figures 2-8 As shown, this is a preferred embodiment of the multi-strand flow wound tube heat exchanger of the present invention. This embodiment is basically the same as the first embodiment, except that this embodiment also includes multiple third heat exchange tubes 6, a third tube sheet 7, a support cylinder 8, and a gasket 9.

[0059] There are two third tube sheets 7, which are disposed opposite each other on the side walls of the hemispherical head 102.

[0060] The support cylinder 8 is fitted around the outer periphery of the second straight pipe section 24 of the first group of heat exchange tubes 2 and inside the hemispherical end cap 102, and is fixed relative to the first tube sheet 4 on the hemispherical end cap 102 (the two can be connected by welding). Multiple through holes 80 are spaced apart on the cylinder wall of the support cylinder 8. In this embodiment, multiple through holes spaced apart circumferentially form a group, and there are multiple groups, arranged spaced apart vertically. Furthermore, the through holes between adjacent groups are staggered vertically. For details, please refer to [link to relevant documentation]. Figure 4 .

[0061] Multiple third heat exchange tubes 6 are arranged horizontally (i.e., the second direction described in the claims and specification of this invention) from the inside out around the support cylinder 8 and inside the hemispherical end cap 102, with each end of the third heat exchange tube 6 supported on its corresponding third tube sheet 7. In this embodiment, the multiple third heat exchange tubes 6 are divided into two groups and are arranged in a C-shape with opposite openings on both radial sides of the support cylinder 8, thus completely surrounding the support cylinder 8. For details, please refer to [link to details]. Figure 6 Meanwhile, the overall structure formed by the multiple third heat exchange tubes 6 is smaller at the top and larger at the bottom, thus matching the shape of the hemispherical head 102. In this embodiment, the overall structure formed by the multiple third heat exchange tubes 6 is a truncated cone (i.e., a frustum), so that as many third heat exchange tubes 6 as possible are distributed within the hemispherical head 102 to ensure heat exchange efficiency. For details, please refer to [link to relevant documentation]. Figure 5 The cross-sectional section indicated by the middle arrow B.

[0062] In this embodiment, to better constrain the third heat exchange tube 6, adjacent inner and outer layers of the third heat exchange tube 6, as well as the innermost third heat exchange tube 6 and the support cylinder 8, are constrained together by spacers 9. Each spacer 9 extends along the first direction and is spaced circumferentially. Figure 8 As shown, the gasket 9 has multiple semi-circular grooves 90 spaced apart along its length to constrain the corresponding third heat exchange tube 6. Furthermore, adjacent inner and outer gaskets 9 can be connected by welding (welding locations are shown in the diagram). Figure 8 (The part indicated by the middle arrow A) thus ensures the stability of the overall structure. In use, the shell-side medium can be input from the shell-side nozzle 103 on the hemispherical head 102, exchange heat with the medium in the third heat exchange tube 6, and flow downward through the gaps between each adjacent third heat exchange tube 6 and the through holes 80 on the support cylinder 8 to exchange heat with the first group of heat exchange tubes 2 and the second group of heat exchange tubes 3, and finally output from the shell-side nozzle 103 on the second end 12 of the shell-side cylinder 1.

[0063] Example 3:

[0064] like Figure 9As shown, this is a preferred embodiment three of the multi-strand flow wound tube heat exchanger of the present invention. This embodiment is basically the same as embodiment two, except that the third heat exchange tube 6 is constrained by the cooperation of the gasket 9 and the tube clamp 91. The cooperation between the gasket 9 and the tube clamp 91 is the same as the prior art, and will not be described in detail here.

[0065] The specification and claims of this invention use terms indicating direction, such as "front," "rear," "upper," "lower," "left," "right," "side," "top," and "bottom," to describe various exemplary structural parts and elements of the invention. However, these terms are used herein merely for ease of explanation and are determined based on the exemplary orientations shown in the accompanying drawings. Since the embodiments disclosed in this invention can be arranged in different orientations, these terms indicating direction are for illustrative purposes only and should not be considered as limitations. For example, "upper" and "lower" are not necessarily limited to directions opposite to or consistent with the direction of gravity.

[0066] The term "vertical" is also used in the specification and claims of this invention, meaning basically along the up and down direction, and is not limited to just the vertical direction, but can also be slightly deviated from the vertical direction.

[0067] The term "radial" is also used in the specification and claims of this invention, meaning essentially along the inside-out direction, and is not limited to the radial direction that passes through the center of the circle, but can also be slightly deviated from the radial direction.

Claims

1. A multi-strand flow-wound heat exchanger, comprising: a shell side cylinder (1) having a first end (11), a second end (12) and a middle part (13) between the first end (11) and the second end (12), and the axial direction of the shell side cylinder (1) is the first direction and the radial direction is the second direction; two groups of heat exchange tubes, namely a first group of heat exchange tubes (2) and a second group of heat exchange tubes (3), which are spirally wound in the shell side cylinder (1) along the first direction; two first tube sheets (4), which are respectively arranged on the first end (11) and the second end (12) of the shell side cylinder (1) to support the two ends of the first group of heat exchange tubes (2) ; two second tube sheets (5), which are arranged on the shell side cylinder (1) corresponding to the two ends of the second group of heat exchange tubes (3) to support the two ends of the second group of heat exchange tubes (3) ; characterized in that: the length of the second group of heat exchange tubes (3) in the first direction is less than the length of the first group of heat exchange tubes (2) in the first direction, and the second group of heat exchange tubes (3) is arranged corresponding to a part of the first group of heat exchange tubes (2) ; at least one of the two second tube sheets (5) is arranged on the side wall of the middle part (13) of the shell side cylinder (1) ; further comprising: a plurality of third heat exchange tubes (6), which are arranged in the shell side cylinder (1) on the periphery of the end of the first group of heat exchange tubes (2) along the second direction; two third tube sheets (7), which are oppositely arranged on the radial sides of the shell side cylinder (1) and adjacent to the first tube sheets (4) for supporting the end of the first group of heat exchange tubes (2) to support the two ends of the third heat exchange tubes (6) ; the plurality of third heat exchange tubes (6) are divided into two groups and are arranged on the radial sides of the end of the first group of heat exchange tubes (2) from the inside to the outside in a C-shaped manner with the C-shaped openings opposite to each other, thereby wholly surrounding the end of the first group of heat exchange tubes (2).

2. The multi-stream spiral wound pipe heat exchanger of claim 1, wherein: The first group of heat exchange tubes (2) has a first spiral section (21) and a second spiral section (22) arranged along the first direction, and the second group of heat exchange tubes (3) is arranged corresponding to the first spiral section (21).

3. The multi-stream spiral wound pipe heat exchanger of claim 2, wherein: The part of the shell side cylinder (1) where the first spiral section (21) of the first group of heat exchange tubes (2) and the second group of heat exchange tubes (3) are located is referred to as the first part (1a), and the part of the shell side cylinder (1) where the second spiral section (22) of the first group of heat exchange tubes (2) is located is referred to as the second part (1b), and the inner diameter of the first part (1a) is greater than the inner diameter of the second part (1b).

4. The multi-stream spiral wound pipe heat exchanger of claim 3, wherein: The first group of heat exchange tubes (2) further has a first straight tube section (23) between the first spiral section (21) and the second spiral section (22) to connect the first and second spiral sections (22).

5. The multi-stream spiral wound pipe heat exchanger of claim 4, wherein: The first straight tube section (23) is arranged corresponding to the first part (1a) of the shell side cylinder (1).

6. The multi-stream spiral wound pipe heat exchanger of claim 5, wherein: One of the second tube sheets (5) is arranged on the side wall of the middle part (13) of the shell side cylinder (1) corresponding to the first straight tube section (23).

7. The multi-stream, spiral wound pipe heat exchanger of claim 5, wherein: A manhole (10) for personnel access is arranged on the side wall of the first part (1a) of the shell side cylinder (1) corresponding to the position of the first straight tube section (23).

8. The multi-stream spiral wound pipe heat exchanger according to any one of claims 3 to 7, characterized in that: The shell side cylinder (1) is vertically arranged, and the first part (1a) and the second part (1b) of the shell side cylinder (1) are arranged one below the other.

9. The multi-stream spiral wound pipe heat exchanger according to any one of claims 1 to 7, characterized in that: The first group of heat exchange tubes (2) are spirally wound into multiple layers of spiral tubes from the inside to the outside, and the second group of heat exchange tubes (3) are spirally wound in each layer of spiral tubes along the spiral direction of the first group of heat exchange tubes (2).

10. The multi-stream, spiral wound pipe heat exchanger of any one of claims 1-7, wherein: The end of the first group of heat exchange tubes (2) is a second straight tube segment (24) extending in the first direction. Further comprising: A support cylinder (8) is sleeved on the outer periphery of the second straight tube segment (24) and is fixed relative to the first tube plate (4) for supporting the end of the first group of heat exchange tubes (2), and a plurality of through holes (80) are distributed on the cylinder wall of the support cylinder (8) at intervals. The third heat exchange tube (6) is arranged around the periphery of the support cylinder (8).

11. The multi-stream, spiral wound pipe heat exchanger of claim 10, wherein: The inner and outer adjacent layers of third heat exchange tubes (6) and the innermost layer of third heat exchange tubes (6) and the support cylinder (8) are constrained together by the spacer strips (9), and each spacer strip (9) extends in the first direction.

12. The multi-stream, spiral wound pipe exchanger of any one of claims 1-7, wherein: The shell side cylinder (1) comprises a straight cylinder (101) extending in the first direction and a hemispherical head (102) arranged on the port of the straight cylinder (101), the end of the hemispherical head (102) is provided with the first tube plate (4) described above, the side wall of the hemispherical head (102) is provided with the third tube plate (7) described above and the shell side connecting pipe (103) for the shell side medium to pass through; The third heat exchange tube (6) is arranged in the hemispherical head.

13. The multi-stream, spiral wound pipe heat exchanger of claim 12, wherein: The hemispherical head (102) is located at the upper end of the straight cylinder (101), and the whole after being surrounded by a plurality of third heat exchange tubes (6) has a structure of small upper end and large lower end, thereby matching the shape of the hemispherical head (102).

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